Results 131 to 140 of about 187 (146)
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Nonlinearity, 2008
In this work, we focus on the multifractal centred Hausdorff measure and the multifractal packing measure in . We find that for 0 < s < t < 2, q < 1, then there exist a set and a probability measure μ on such that and, in addition,
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In this work, we focus on the multifractal centred Hausdorff measure and the multifractal packing measure in . We find that for 0 < s < t < 2, q < 1, then there exist a set and a probability measure μ on such that and, in addition,
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Exact Hausdorff and packing measures of Cantor sets with overlaps
Ergodic Theory and Dynamical Systems, 2014Let $K$ be the attractor of a linear iterated function system (IFS) $S_{j}(x)={\it\rho}_{j}x+b_{j},j=1,\ldots ,m$, on the real line $\mathbb{R}$ satisfying the generalized finite type condition (whose invariant open set ${\mathcal{O}}$ is an interval) with an irreducible weighted incidence matrix. This condition was recently introduced by Lau and Ngai [
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Chaos, Solitons & Fractals, 2005
The authors establish Frostman-type lemmas for the Hausdorff and pre-packing measures on a product probability measure space \((\Omega, {\mathcal F}, \mu) = (\Omega_1\times \Omega_2, {\mathcal F}_1\times {\mathcal F}_2, \mu_1\times\mu_2)\). Based on these results, they prove a sufficient condition for the Hausdorff and packing dimensions with respect ...
Dai, Chaoshou, Hou, Yanyan
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The authors establish Frostman-type lemmas for the Hausdorff and pre-packing measures on a product probability measure space \((\Omega, {\mathcal F}, \mu) = (\Omega_1\times \Omega_2, {\mathcal F}_1\times {\mathcal F}_2, \mu_1\times\mu_2)\). Based on these results, they prove a sufficient condition for the Hausdorff and packing dimensions with respect ...
Dai, Chaoshou, Hou, Yanyan
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The branching measure, Hausdorff and packing measures on the Galton-Watson tree
2000We present some recent results concerning the branching measure, the exact Husdorff measure and the exact packing measure, defined on the boundary of the Caalton-Watson tree. The results show that in good cases, these three measures coincide each other up to a constant, that the branching measure is homogeneous (it has the same local dimension at each ...
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Hausdorff and packing dimensions, intersection measures, and similarities
1999Let \(\mu\) and \(\nu\) be Radon measures on \(\mathbb R^n\) with compact supports. We study the Hausdorff, \(\dim_H\), and packing dimension, \(\dim_p\), properties of the intersection measures \(\mu\cap f_\sharp\nu\) when \(f\) runs through the similarities of \(\mathbb R^n\) and \(f_\sharp\nu\) is the image of \(\nu\) under \(f\). These measures can
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Commentationes Mathematicae Universitatis Carolinae, 2009
Summary: We extend the notions of Hausdorff and packing dimension introducing weights in their definition. These dimensions are computed for ergodic invariant probability measures of two-dimensional Lorenz transformations, which are transformations of the type occuring as first return maps to a certain cross section for the Lorenz differential equation.
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Summary: We extend the notions of Hausdorff and packing dimension introducing weights in their definition. These dimensions are computed for ergodic invariant probability measures of two-dimensional Lorenz transformations, which are transformations of the type occuring as first return maps to a certain cross section for the Lorenz differential equation.
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Regularities of general Hausdorff and packing functions
Chaos, Solitons and Fractals, 2019Bilel Selmi, Zied Douzi
exaly